Search

Since in nature there are species that take refuge, totally or proportionally, from the predator if the prey population size exceeds a threshold value, and become available again to the predator, with linear predator functional response, if its population size is higher than the threshold value, in this work we show all the changes in the dynamics presented by two discontinuous Leslie–Gower predator–prey models, assuming harvesting and alternative food for predators and total protection, or a constant proportional refuge of prey from being consumed by the predator when its population size is below the threshold value. The conditions on their parameters to determine the dynamics of each discontinuous model are developed by means of a bifurcation analysis, with respect to the threshold value of the prey population size and the collection rate for predators. It is concluded that for certain conditions on their parameters, the prey population size could reach a convergence equal or higher than its threshold value when considering the discontinuous model with a mechanism to protect prey from being consumed by the predator, as opposed to the discontinuous model with a constant proportion of prey refuges above the threshold value, whose convergence could be lower, equal or higher than the threshold value. [ABSTRACT FROM AUTHOR]

This paper investigates a stochastic SIR epidemic model for the Hepatitis B virus (HBV), which includes two types of white noise disturbances that influence both disease transmission and recovery rates. We use Lyapunov functions to establish the solution's global existence and positivity. In addition, we investigate conditions for HBV extinction and uniform persistence, using appropriate Lyapunov functions to assess model stability. Numerical simulations show that fluctuations in the disease transmission are directly related to the intensity of the noise disturbances. This insight suggests effective control strategies for managing HBV dynamics. Furthermore, we conclude that stochastic disturbances have a significant impact on disease transmission, and in some cases, increased noise intensity may help limit the spread of infection. • Two-dimensional stochastic SIR model for Hepatitis B. • Global solution and positivity. • Extinction and persistence. • Impact of noise on transmission. • Practical implications for disease control. [ABSTRACT FROM AUTHOR]

In the present study, we develop a model for hepatitis B virus (HBV) that integrates cell-to-cell transmission of the virus, CTL immunological response, delay effects, and the effect of fluctuating environmental noise. The inheritance randomness of the system shifting the system from a deterministic to another system consists of stochastic differential equations (SDEs). After model formulation, the dynamical aspects of the model are investigated by using the key threshold quantity R 0. If the threshold value R 0 is assumed less than unity, then it is proven that the solution trajectories are fluctuating around the disease-free state (DFS) of the associated deterministic model. The fluctuation of the trajectories around the DFS explains the phenomenon of extinction of the stochastic models. It is also proved that the trajectories of the SDE model oscillate around the endemic state of the underlying ODE system when R 0 s > 1 explains the sure persistence theory of the proposed model. One notable finding of the present manuscript is the positive association between the fluctuating amplitude and the intensities of the white noises. This understanding can provide useful control tools for managing the worst dynamic(s) of the infection. The exact value of the parameter for time delay determines the stability of the model under consideration. By analyzing the time-delayed parameter, it was identified that the model is stable by keeping the value of the parameter below the crucial value that causes the Hopf bifurcation. This conclusion is supported by the numerical examples having epidemiological significance. Furthermore, the findings suggest that stochastic environmental disturbance can impact the spread of infectious illnesses. Notably, the high levels of noise can help to slow down the spread of epidemics in the population. • A mathematical model is presented to describe the impact of cell-to-cell transmission of HBV. • The ergodic stationary distribution exists under certain conditions. • The proposed mathematical model is investigated with a time delay parameter. • Studies the dynamics of cell-to-cell transmission with time delay. • Numerical simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to establish a novel three-way decisions-based grey incidence analysis clustering approach and exploit it to extract information and rules implied in panel data. Design/methodology/approach: Because of taking on the spatiotemporal characteristics, panel data can well-describe and depict the systematic and dynamic of the decision objects. However, it is difficult for traditional panel data analysis methods to efficiently extract information and rules implied in panel data. To effectively deal with panel data clustering problem, according to the spatiotemporal characteristics of panel data, from the three dimensions of absolute amount level, increasing amount level and volatility level, the authors define the conception of the comprehensive distance between decision objects, and then construct a novel grey incidence analysis clustering approach for panel data and study its computing mechanism of threshold value by exploiting the thought and method of three-way decisions; finally, the authors take a case of the clustering problems on the regional high-tech industrialization in China to illustrate the validity and rationality of the proposed model. Findings: The results show that the proposed model can objectively determine the threshold value of clustering and achieve the extraction of information and rules inherent in the data panel. Practical implications: The novel model proposed in the paper can well-describe and resolve panel data clustering problem and efficiently extract information and rules implied in panel data. Originality/value: The proposed model can deal with panel data clustering problem and realize the extraction of information and rules inherent in the data panel. [ABSTRACT FROM AUTHOR]

An age-structured juvenile-adult model with impulsive harvesting is developed on a periodically evolving domain. The principal eigenvalue is firstly defined by Krein–Rutman theorem on a Banach space involving impulse and its properties are explicitly discussed. Moreover, sufficient conditions for the solution to persist or extinct are presented by comparison principle with impulse. The final numerical simulations are carried out to verify our analytical findings. Our results imply that harvesting pulse can make individuals from persistence to struggle to survive, or from extinction to rapidly extinction. Moreover, small rate of regional evolution are detrimental to species persistence, that is, small evolutional rate turns individuals from persistence to extinction. • The impulsive harvesting and evolving domain are firstly introduced in a juvenile-adult model. • The principal eigenvalue in a Banach space involving impulse is given. • The impacts of impulsive harvesting and evolving domain are presented. [ABSTRACT FROM AUTHOR]

Abstract: The technological changes and educational expansion have created the heterogeneity in the human species. Clearly, this heterogeneity generates a structure in the population dynamics, namely: citizen, permanent resident, visitor, and etc. Furthermore, as the heterogeneity in the population increases, the human mobility between meta-populations patches also increases. Depending on spatial scales, a meta-population patch can be decomposed into sub-patches, for examples: homes, neighborhoods, towns, etc. Members of the population can move between the sub-patches. The dynamics of human mobility in a heterogeneous and scaled structured population is still its infancy level. In this work, an attempt is made to investigate the human mobility dynamics of heterogeneous and scaled structured population. We present a two scaled human mobility model for a meta-population. The sub regions and regions are interlinked via intra-and inter regional transport network systems. Under various types of growth order assumptions on the intra and interregional residence times of the residents of a sub region, different patterns of static behavior of the mobility process is studied. In addition, the results reveal that the system has a natural tendency to quarantine itself without total breaking a link in the transportation network system. Moreover, there is a threshold point for the largest intra regional visiting time of residents of a given sub region that leads to either a total isolation of the residents from other sub regions within the region or a partial isolation of residents from some of the sub regions within the region. [ABSTRACT FROM AUTHOR]

Similar to other epidemics, the novel coronavirus (COVID-19) spread very fast and infected almost two hundreds countries around the globe since December 2019. The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere. Assuming that the spread of virus follows a random process instead of deterministic. The continuous time Markov Chain (CTMC) through stochastic model approach has been utilized for predicting the impending states with the use of random variables. The proposed study is devoted to investigate a model consist of three exclusive compartments. The first class includes white nose based transmission rate (termed as susceptible individuals), the second one pertains to the infected population having the same perturbation occurrence and the last one isolated (quarantined) individuals. We discuss the model's extinction as well as the stationary distribution in order to derive the the sufficient criterion for the persistence and disease' extinction. Lastly, the numerical simulation is executed for supporting the theoretical findings. [ABSTRACT FROM AUTHOR]